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Geometric transitions : from hyperbolic to Ads geometry

著者: Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
出版商: 2011.
论文: Thesis (Ph. D.)--Stanford University, 2011.
版本/格式:   硕士/博士论文 : 文献 : 硕士论文/博士论文 : 电子图书   计算机文档 : 英语
数据库:WorldCat
提要:
We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path into AdS structures. In particular, when hyperbolic cone manifolds collapse, the AdS manifolds  再读一些...
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材料类型: 文献, 硕士论文/博士论文, 互联网资源
文件类型: 互联网资源, 计算机文档
所有的著者/提供者: Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
OCLC号码: 743406573
注意: Submitted to the Department of Mathematics.
描述: 1 online resource.
责任: Jeffrey Danciger.

摘要:

We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path into AdS structures. In particular, when hyperbolic cone manifolds collapse, the AdS manifolds generated on the "other side" of the transition have tachyon singularities. The method involves the study of a new transitional geometry called half-pipe geometry. We also discuss combinatorial/algebraic tools for constructing transitions using ideal tetrahedra. Using these tools we prove that transitions can always be constructed when the underlying manifold is a punctured torus bundle.

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